That is used as an indication and not an actual last name. Garrosh is his only name, the title "Son of Hellscream" was used as a way to show that he is the child of Hellscream, but so far Garrosh has no last name.

Now Jorin Deadeye is another story, as he actually adopted the last name of his father. I would like to hear why he did such a thing.

Because Deadeye is probably the most known chieftain even if people don't realize that he's a chieftain. The whole eye of Kilrogg thing...